On the Higher Moments of Particle Multiplicity, Chemical Freeze-Out, and QCD Critical Endpoint

Abstract

We calculate the first six non-normalized moments of particle multiplicity within the framework of the hadron resonance gas model. In terms of the lower order moments and corresponding correlation functions, general expressions of higher order moments are derived. Thermal evolution of the first four normalized moments and their products (ratios) are studied at different chemical potentials , so that it is possible to evaluate them at chemical freeze out curve. It is found that a non-monotonic behaviour, reflecting the dynamical fluctuation and strong correlation of particles starts to appear from the normalized third order moment. We introduce novel conditions for describing the chemical freeze out curve. Although the hadron resonance gas model does not contain any information on the criticality related to the chiral dynamics and singularity in the physical observables, we are able find out the location of the QCD critical endpoint at µ ∼ 350 MeV and temperature T ∼ 162 MeV.Recently, the higher order multiplicity moments have gained prominence in high energy physics with a huge hope in pinpointing the QCD critical endpoint (CEP) [1] connecting the first order boundary separating the hadronic from the partonic matter at high density with the crossover boundary at low density [2,3]. It is clear that the hadron resonance gas partition function is an approximation to a non-singular part of the free energy of QCD in the hadronic phase. There are large theoretical uncertainties of its location and even its existence is not fully confirmed, yet [4][5][6]. The characteristic feature of CEP are critical dynamical fluctuations [7][8][9][10][11]. The higher order moments are conjectured to reflect the large fluctuations associating the hadronquark phase transition. This was the motivation of a remarkable number of experimental and theoretical studies [1,[12][13][14]. Recently, various calculations have shown that the higher order moments of the multiplicity distributions of some conserved quantities, such as net-baryon, net-charge, and net-strangeness, are sensitive to the correlation length ξ [15-17], which in turn is related to the higher order moments, themselves. In realistic heavy-ion collisions, the correlation length is found to remain finite.Apparently, it should not be an exception that the strongly interacting QCD matter undergoes phase transition(s) at extreme conditions, as almost all matter types suffer from such a critical change as the extreme conditions change. The Lattice QCD calculations predict that a cross-over takes place between the hadronic phase and the Quark Gluon Plasma (QGP) phase, when the temperature exceeds critical value of T c ≃ 150 − 190 MeV. As given in Ref. [3,18], depending on the different parameters (for instance, the quark favours and their masses) and on the lattice configurations, lattice QCD assigns different values to T c . Furthermore, the value of T c depends on the baryon chemical potential µ. With vanishing µ the lattice QCD calculations [19] show that the higher order suscepti...

Hadronic equation of state and speed of sound in thermal and dense medium

“…Another supportive evidence has been reported in Ref. [24]. At high T , formation of resonances is only achieved through strong interactions, the effective mass is assumed to approach the physical one and the strong interactions are conjectured to be taken into consideration through including heavy resonances.…”

“…That no dip appears in HRG would mean that the equilibrium distribution function should be a subject of modification [20,45]. Last but not least, the higher moments have to be estimated for the lattice data, in order to understand its structure [24].…”

“…This is not reflected in the HRG results. A precise judgement about the dataset and its structure would be achievable through the normalized higher moments [24]. In lattice QCD as well as in HRG, there is a qualitative tendency that c 2 s slightly decrease with increasing T up to ∼ 150 MeV.…”

“…This model seems to provide a good description for the thermal evolution of the thermodynamic quantities in the hadronic matter [12][13][14][15][16][17][18][19][20][21] and has been successfully utilized to characterize the conditions deriving the chemical freeze-out at finite densities [22][23][24]. In light of this, the HRG model can be used in calculating the speed of sound using a grand canonical partition function of an ideal gas with all experimentally observed states up to a certain large mass as constituents.…”

Fluctuations and correlations of conserved charges in an excluded-volume hadron resonance gas model

“…Hence along the freeze-out line one would expect a non-monotonic behaviour of the quantities given in Eq. 16 [62,77]. To compare the products of moments with experiment one has to know freeze-out T and µ at a particular √ s N N .…”